Answer:
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<h2>Given</h2>
<h3>Line 1</h3>
<h3>Line 2</h3>
- Passing through the points (4, 3) and (5, - 3)
<h2>To find</h2>
- The value of k, if the lines are perpendicular
<h2>Solution</h2>
We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.
Find the slope of line 1 by converting the equation into slope-intercept from standard form:
<u><em>Info:</em></u>
- <em>standard form is ⇒ ax + by + c = 0, </em>
- <em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>
- 3x - ky + 7 = 0
- ky = 3x + 7
- y = (3/k)x + 7/k
Its slope is 3/k.
Find the slope of line 2, using the slope formula:
- m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6
We have both the slopes now. Find their product:
- (3/k)*(- 6) = - 1
- - 18/k = - 1
- k = 18
So when k is 18, the lines are perpendicular.
The answer is 1.12% decrease
Explanation in image
Make a proportion.
Do base over height;
.
h is the height of the second triangle. Solve for h.
Cross multiply.
6h = 168
h = 28
The height of the second triangle is 28 cm.
Half-life, h = 13 hours
Mass initial, a = 38 g
B=base for half-life = 2
(a)
I(t)=a*B^(-t/h)=a*(B^(1/h)^(-t)=a*(B^(-1/13))^t
Substituting values,
I(t)=38*(2^(-1/13))^t
a=38 g
b=2^(-1/13)=0.9480775 (approximately)
=>
I(t)=38*0.9480775^t
(b) I(t)=7
solve
I(t)=7=38*0.948077^t
Take log on both sides and solve for t
t=log(7/38)/log(0.948077)
=31.727 hours.
Check: I(31.727)=38*9.948077^(31.727)=7.000 g ok
